An Improved Algorithm for Diameter-Optimally Augmenting Paths in a Metric Space

Abstract

Let P be a path graph of n vertices embedded in a metric space. We consider the problem of adding a new edge to P such that the diameter of the resulting graph is minimized. Previously (in ICALP 2015) the problem was solved in \(O(n\log ^3 n)\) time. In this paper, based on new algorithmic techniques and observations, we present an \(O(n\log n)\) time algorithm.